Lobbying itself is not bribery, it's just speaking to people who have power and trying to influence them. Political contributions by lobbyists are not bribery for a couple of reasons:
1) The money is not a quid pro quo. You don't hand a check to politician and then tell them how to vote, and politicians do not always vote depending on who gave them money. Now yes, a politician is probably going to be influenced by big donors, but not always. If they don't side with you, then you can decide not to donate again. But you can't ask for your money back, or threaten them because you paid them and they didn't do what you wanted. Thus the only incentive to side with you (aside from your incredibly persuasive intellectual arguments) is that you MAY donate to their campaign again. Oppositely, once you've made a contribution, they have your money and can do what they please. You can't get it back.
2) The money is tracked. Campaigns are required to disclose who gave them money. Lobbyists are required to disclose who they gave money to, and they are required to disclose who pays them to lobby.
3) The money is limited (at least for direct contributions to a campaign). There is a limit to how much each individual and business can give to a single campaign. PACs and other organizations are another story for another time.
What the money does do is it buys access. Campaign donors, especially larger ones, are more likely to get a meeting quickly with a lawmaker or have their calls taken. I say quickly because anyone can ask for and get a meeting, but whether or not you've donated to their campaign and may be likely to do so in the future can influence whether a lawmaker decides to meet with you or not. Also, fundraisers (where you bring a check and the lawmaker is there) are easy ways to get 5-10 minutes of facetime with a person in power.
Edit: One additional point: There are laws about how you can spend campaign contributions. Legally, you can only use them for campaign expenditures (ads, signs, paying workers, etc.). Thus you cannot use them to buy yourself a nice new car or watch. Yes, this does happen, but its a violation of campaigning laws, again, not bribery.
Credit: u/mct137